In printing machine inking units one common problem is to supply a uniform thin film of ink to the printing plate over its entire length. In many instances, however, the ink distribution is so unfavorable that uniformity cannot be completely achieved, so that printing errors occur in the form of visible ink intensity differences or "mottling". In an attempt to obviate mottling, in a known inking unit for printing machines such as disclosed in German patent specification 30 34 644, the last ink applicator roller in the direction of rotation of the cylinder and another ink applicator roller are constructed as distributing rollers which perform a side traverse motion and the frequency of movement of which differs from whichever of the ink distributing rollers is in contact at any time. The disadvantage of this known inking unit is that the side traverse movement of the applicator rollers may cause distortion and increased size of the screen dots, particularly at high printing speeds, thus impairing the print quality. Also, the standstill on the change of direction of the side traverse movement may cause printing errors.